Time-sharing analysis combining processor scheduling and memory resources

Abstract

Considering time-sharing as a stochastic queuing process, a probabilistic model of an infinite source round robin time-shared system is formulated and studied under a variety of circumstances. At first, a continuous process is considered using independent Poisson arrivals and exponential service. Assumptions include positive overhead time and explicit fixed priorities or bribes chosen a priori by the user of the system without any specific knowledge of the state of the system at the time he seeks to submit his job. For analytical convenience, a Markov chain is embedded within the continuous system and analysis proceeds via the method of generating functions on the discrete renewal points of the Markov sequence. Performance measures derived include the first and second moments for the state variable (number of tasks in the system) at stationarity, waiting time moments both for the job queue and the entire system conditioned on a known service requirement and the mean of the first response for user requests belonging to a given priority class.